One of the main challenges in the numerical simulation of wave scattering problems, over infinite or semi-infinite domains, is the proper imposition of radiation boundary conditions: When the analysis is performed using a full domain method, e.g., the finite differences method (FDM) or the finite element method (FEM), one has to render finite the computational domain, and use artificial boundary elements to approximate radiation damping. A wide variety of absorbing boundary elements are available in the literature, [1]}, [2]}, [3]}. Most of these elements suffer deficiencies, like dependence of the performance on the angle of the incident wave or a limited frequency band of efficient operation. On the other hand, among the many techniques available to approximate Sommerfeld's radiation boundary conditions, those based on integral formulations are the most accurate [4]}, [5]}, [6]}; although their coupling to existing finite element codes introduces inconvenient features, since their resulting coefficient matrices are asymmetric and fully populated and destroy many of the appealing features of finite element methods. In this work we explore approximations to the radiation boundary condition, that combine the accuracy of integral-based formulations with the advantages of the finite element algorithm. Our approximate representation is intended to be useful in the solution of scattering problems of moderate size using existing finite element codes and the resources available in current personal computers.
